Properties

Label 380.2.v
Level $380$
Weight $2$
Character orbit 380.v
Rep. character $\chi_{380}(7,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $224$
Newform subspaces $3$
Sturm bound $120$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 380 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(380, [\chi])\).

Total New Old
Modular forms 256 256 0
Cusp forms 224 224 0
Eisenstein series 32 32 0

Trace form

\( 224 q - 2 q^{2} - 4 q^{5} - 20 q^{8} + O(q^{10}) \) \( 224 q - 2 q^{2} - 4 q^{5} - 20 q^{8} - 2 q^{10} + 4 q^{12} - 4 q^{13} - 4 q^{17} - 64 q^{20} - 8 q^{21} + 22 q^{22} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 12 q^{30} - 12 q^{32} + 8 q^{33} - 68 q^{36} - 16 q^{37} - 30 q^{38} + 8 q^{40} - 16 q^{41} + 30 q^{42} - 56 q^{45} + 24 q^{46} - 28 q^{48} + 12 q^{50} - 18 q^{52} - 4 q^{53} - 16 q^{56} - 12 q^{57} - 140 q^{58} + 14 q^{60} - 72 q^{61} + 12 q^{62} - 48 q^{65} - 12 q^{66} + 4 q^{68} - 82 q^{70} + 56 q^{72} - 4 q^{73} + 60 q^{76} + 48 q^{77} + 48 q^{78} - 2 q^{80} + 40 q^{81} + 16 q^{82} + 20 q^{85} + 64 q^{86} + 104 q^{88} - 92 q^{90} + 4 q^{92} - 24 q^{93} - 32 q^{96} - 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(380, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.2.v.a 380.v 380.v $4$ $3.034$ \(\Q(\zeta_{12})\) None 380.2.v.a \(-4\) \(6\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\zeta_{12}^{3})q^{2}+(2-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
380.2.v.b 380.v 380.v $4$ $3.034$ \(\Q(\zeta_{12})\) None 380.2.v.a \(2\) \(-6\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+\zeta_{12}+\cdots)q^{3}+\cdots\)
380.2.v.c 380.v 380.v $216$ $3.034$ None 380.2.v.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$